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Attention:
Only (N+).
Fermat's last Theorem z ^ 3 = x ^ 3 + y ^ 3 is capable exists a solution if fully meet the following conditions:
First step:
(1+2+3+4+........+a)^2+(1+2+3+4+........+b)^2=v^2.
In fact, using the computer, this equation has the ability to survive.
Second step:
(1+2+3+4+........+a+1)^2+(1+2+3+4+........+b+1)^2=s^2.
Third step:
v=1+2+3+4+........+c.
In fact, using the computer, this equation has the ability to survive.
Fourth step:
s=1+2+3+4+........d.
Fifth step:
d=c+1
If all five steps are satisfied.This equation is capable of existence.
[z(z+1)/2]^2 - [z(z-1)/2]^2=[x(x+1)/2]^2- [x(x-1)/2]^2+[y(y+1)/2]^2 - [y(y-1)/2]^2.
Because:
z^3=[z(z+1)/2]^2 - [z(z-1)/2]^2.
Mean this equation is capable of existence.
z^3=x^3+y^3.
However, too hard to satify all five equations in same time..
And more:
Attention about series of number:
1,3,6,10,15,21,28,36,45........
Recognize:
10 and 15 are two number consecutive which belong this string.
Having:
15^2 - 10^2=5^3.
Or:
z^3=[z(z+1)/2]^2 - [z(z-1)/2]^2.
Impossible in same time exist both:
[z(z+1)/2]^2=[x(x+1)/2]^2+[y(y+1)/2]^2
And
[z(z-1)/2]^2=[x(x-1)/2]^2+[y(y-1)/2]^2
Attention:
All numbers as z(z+1)/2 and x(x+1)/2 and y(y+1)/2 and z(z-1)/2 and x(x-1)/2 and y(y-1)/2 are belong this string and they are Pythagorean
This is main proof:
z^3=[z(z+1)/2]^2 - [z(z-1)/2]^2
Define:
x<x+a<y.
x^3+y^3=[y(y+1)/2]^2 - [x(x-1)/2]^2 - [(x+1)^3+(x+2)^3+........+(x+a-1)^3+(x+a)^3+(x+a+1)^3+........+(y-1)^3]
Suppose:
z^3=x^3+y^3.
Because also:
(x+a)^3= [(x+a)(x+a+1)/2]^2 - [(x+a)(x+a-1)/2]^2.
Therefore a system of equations is generated.
[z(z+1)/2]^2 - [z(z-1)/2]^2=[y(y+1)/2]^2 - [x(x-1)/2]^2 - [(x+a)(x+a+1)/2]^2 + [(x+a)(x+a-1)/2]^2 - [(x+1)^3+(x+2)^3+........+(x+a-1)^3+(x+a+1)^3+........+(y-1)^3]
[z(z+1)/2]^2 - [z(z-1)/2]^2=[y(y+1)/2]^2 - [x(x-1)/2]^2 - [(x+b)(x+b+1)/2]^2 + [(x+b)(x+b-1)/2]^2 - [(x+1)^3+(x+2)^3+........+(x+b-1)^3+(x+b+1)^3+........+(y-1)^3]
[z(z+1)/2]^2 - [z(z-1)/2]^2=[y(y+1)/2]^2 - [x(x-1)/2]^2 - [(x+c)(x+c+1)/2]^2 + [(x+c)(x+c-1)/2]^2 - [(x+1)^3+(x+2)^3+........+(x+c-1)^3+(x+c+1)^3+........+(y-1)^3]
[z(z+1)/2]^2 - [z(z-1)/2]^2=[y(y+1)/2]^2 - [x(x-1)/2]^2 - [(x+d)(x+d+1)/2]^2 + [(x+d)(x+d-1)/2]^2 - [(x+1)^3+(x+2)^3+........+(x+d-1)^3+(x+d+1)^3+........+(y-1)^3].
........
Can not count the number of equations
And more;
Using the two formulas by rotation affect each other:
z^3=[z(z+1)/2]^2 - [z(z-1)/2]^2
And
[z(z+1)/2]^2=1^3+2^3+........+z^3.
This method makes root equation z^3=x^3+y^3 is structured as a Transfiguration equation which having unlimited formats as Robot Bumblebee Transformer.
Similar,this method is used for general case:
z ^ n = x ^ n + y ^ n.
Mean:
z ^ (n-3) * z ^ 3 = x ^ (n-3) * x ^ 3 + y ^ (n-3) * y^ 3.
You can structure this equation according to your own discretion when use z^3=[z(z+1)/2]^2 - [z(z-1)/2]^2 then use [z(z+1)/2]^2=1^3+2^3+........+z^3 then continue by same to become your own format.
ADIEU.
What else can I help you with?
Who is person who is solving Fermat?
Andrew Wiles solved/proved Fermats Last Theorem. The theorem states Xn + Yn = Zn , where n represents 3, 4, 5,......... there is no solution.
What is fermats last theorem?
Fermat's Last Theorem is sometimes called Fermat's conjecture. It states that no three positive integers can satisfy the equation a*n + b*n = c*n, for any integer n greater than two.
What is the number that no value of can be greater than for the solutions to the equation in fermats last theorem?
Fermat's last theorem states that the equation xn + yn = zn has no integer solutions for x, y and z when the integer n is greater than 2. When n=2, we obtain the Pythagoras theorem.
Did anyone oppose to the pythgreom theorm?
Although the Pythagorean theorem (sums of square of a right angled triangle) is called a theorem it has many mathematical proofs (including the recent proof of Fermats last theorem which tangentially also prooves Pythagorean theorem). In fact Pythagorean theorem is an 'axiom', a kind of 'super law'. It doesn't matter if anyone does oppose it, it is one of the few fundamental truths of the universe.
Was Fermat's Last Theorem really his last theorem?
This was not the last theorem that Fermat wrote. Rather, it was the last one to be proven/disproven.
How many pages does The Last Theorem have?
The Last Theorem has 311 pages.
When was The Last Theorem created?
The Last Theorem was created in 2008-07.
Why wasn't Fermats last theorem written on paper?
But it was. That is why we know about it. If you mean why the PROOF was not written- Fermat wrote that he had found a wonderful proof for the theorem, but unfortunately the margin was too small to contain it. This is why the theorem became so famous- being understandable by even a schoolchild, but at the same time so hard to prove that even the best mathematicians had to surrender, with a simple proof seemingly being existent that just nobody except Fermat could find. The theorem has since been proven but the proof uses math tools that are very advanced and were not available in Fermat's life-time.
What is a Theorem ender?
QED, Fermat's Last Theorem.
What is the ISBN of The Last Theorem?
The ISBN of The Last Theorem is 978-0-00-728998-1.
What Great Mathematicians are still alive?
Andrew Wiley, who solved Fermat's Last Theorem. Andrew Wiley, who solved Fermat's Last Theorem.
What year was Fermat's last theorem?
1637
